Inheritance diagram for nzmath.intresidue.IntegerResidueClassRing:

Collaboration diagram for nzmath.intresidue.IntegerResidueClassRing:

Public Member Functions
def	__init__ (self, modulus)

def	__repr__ (self)

def	__str__ (self)

def	__hash__ (self)

def	card (self)

def	getInstance (cls, modulus)

def	createElement (self, seed)

def	getCharacteristic (self)

def	__contains__ (self, elem)

def	isfield (self)

def	__eq__ (self, other)

def	__ne__ (self, other)

def	issubring (self, other)

def	issuperring (self, other)

Public Member Functions inherited from nzmath.ring.CommutativeRing
def	__init__ (self)

def	getQuotientField (self)

def	isdomain (self)

def	isnoetherian (self)

def	isufd (self)

def	ispid (self)

def	iseuclidean (self)

def	registerModuleAction (self, action_ring, action)

def	hasaction (self, action_ring)

def	getaction (self, action_ring)

Public Member Functions inherited from nzmath.ring.Ring
def	getCommonSuperring (self, other)

Public Attributes
	m

Public Attributes inherited from nzmath.ring.CommutativeRing
	properties

Static Public Attributes
def	isdomain = isfield

def	isnoetherian = isfield

def	isufd = isfield

def	ispid = isfield

def	iseuclidean = isfield

Properties
	one = property(_getOne, None, None, "multiplicative unit.")

	zero = property(_getZero, None, None, "additive unit.")

Private Member Functions
def	_getOne (self)

def	_getZero (self)

Private Attributes
	_one

	_zero

Static Private Attributes
dictionary	_instances = {}

Detailed Description

IntegerResidueClassRing is also known as Z/mZ.

Definition at line 218 of file intresidue.py.

Constructor & Destructor Documentation

◆ init()

def nzmath.intresidue.IntegerResidueClassRing.__init__	(	self,
		modulus
	)

The argument modulus m specifies an ideal mZ.

Definition at line 225 of file intresidue.py.

Member Function Documentation

◆ contains()

def nzmath.intresidue.IntegerResidueClassRing.__contains__	(	self,
		elem
	)

Definition at line 277 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ eq()

def nzmath.intresidue.IntegerResidueClassRing.__eq__	(	self,
		other
	)

Equality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 302 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

Referenced by nzmath.poly.multivar.TermIndices.__ne__(), nzmath.poly.ring.PolynomialRing.__ne__(), nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.poly.formalsum.FormalSumContainerInterface.__ne__(), nzmath.poly.array.ArrayPoly.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

◆ hash()

def nzmath.intresidue.IntegerResidueClassRing.__hash__ ( self )

Reimplemented from nzmath.ring.Ring.

Definition at line 242 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ ne()

def nzmath.intresidue.IntegerResidueClassRing.__ne__	(	self,
		other
	)

Inequality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 307 of file intresidue.py.

◆ repr()

def nzmath.intresidue.IntegerResidueClassRing.__repr__ ( self )

Definition at line 236 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ str()

def nzmath.intresidue.IntegerResidueClassRing.__str__ ( self )

Definition at line 239 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ _getOne()

def nzmath.intresidue.IntegerResidueClassRing._getOne ( self )

private

Definition at line 322 of file intresidue.py.

References nzmath.imaginary.ComplexField._one, nzmath.intresidue.IntegerResidueClassRing._one, nzmath.algfield.NumberField._one, nzmath.finitefield.FinitePrimeField._one, and nzmath.finitefield.ExtendedField._one.

◆ _getZero()

def nzmath.intresidue.IntegerResidueClassRing._getZero ( self )

private

Definition at line 330 of file intresidue.py.

References nzmath.imaginary.ComplexField._zero, nzmath.intresidue.IntegerResidueClassRing._zero, nzmath.algfield.NumberField._zero, nzmath.finitefield.FinitePrimeField._zero, and nzmath.finitefield.ExtendedField._zero.

◆ card()

def nzmath.intresidue.IntegerResidueClassRing.card ( self )

Return the cardinality of the ring.

Definition at line 245 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ createElement()

def nzmath.intresidue.IntegerResidueClassRing.createElement	(	self,
		seed
	)

createElement returns an element of the ring with seed.

Reimplemented from nzmath.ring.Ring.

Definition at line 263 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

Referenced by nzmath.finitefield.FiniteField.random_element(), and nzmath.finitefield.FiniteField.TonelliShanks().

◆ getCharacteristic()

def nzmath.intresidue.IntegerResidueClassRing.getCharacteristic ( self )

The characteristic of Z/mZ is m.

Reimplemented from nzmath.ring.Ring.

Definition at line 271 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ getInstance()

def nzmath.intresidue.IntegerResidueClassRing.getInstance	(	cls,
		modulus
	)

getInstance returns an instance of the class of specified
modulus.

Definition at line 252 of file intresidue.py.

References nzmath.finitefield.FinitePrimeField._instances, and nzmath.intresidue.IntegerResidueClassRing._instances.

◆ isfield()

def nzmath.intresidue.IntegerResidueClassRing.isfield ( self )

isfield returns True if the modulus is prime, False if not.
Since a finite domain is a field, other ring property tests
are merely aliases of isfield.

Reimplemented from nzmath.ring.CommutativeRing.

Definition at line 283 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, nzmath.intresidue.IntegerResidueClassRing.m, and nzmath.ring.CommutativeRing.properties.

◆ issubring()

def nzmath.intresidue.IntegerResidueClassRing.issubring	(	self,
		other
	)

Report whether another ring contains the ring as a subring.

Reimplemented from nzmath.ring.Ring.

Definition at line 310 of file intresidue.py.

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), and nzmath.rational.IntegerRing.getCommonSuperring().

◆ issuperring()

def nzmath.intresidue.IntegerResidueClassRing.issuperring	(	self,
		other
	)

Report whether the ring is a superring of another ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 316 of file intresidue.py.

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.poly.ring.PolynomialRing.getCommonSuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCommonSuperring(), nzmath.poly.ring.RationalFunctionField.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), nzmath.rational.IntegerRing.getCommonSuperring(), nzmath.real.RealField.issubring(), and nzmath.poly.ring.RationalFunctionField.issuperring().

Member Data Documentation

◆ _instances

dictionary nzmath.intresidue.IntegerResidueClassRing._instances = {}

staticprivate

Definition at line 223 of file intresidue.py.

Referenced by nzmath.intresidue.IntegerResidueClassRing.getInstance(), nzmath.poly.ring.PolynomialRing.getInstance(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getInstance(), nzmath.poly.ring.RationalFunctionField.getInstance(), and nzmath.matrix.MatrixRing.getInstance().

◆ _one

nzmath.intresidue.IntegerResidueClassRing._one

private

Definition at line 325 of file intresidue.py.

Referenced by nzmath.poly.ring.PolynomialRing._get_one(), nzmath.poly.ring.RationalFunctionField._get_one(), nzmath.real.RealField._getOne(), nzmath.intresidue.IntegerResidueClassRing._getOne(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables._getOne(), nzmath.ring.ResidueClassRing._getOne(), nzmath.rational.RationalField._getOne(), nzmath.rational.IntegerRing._getOne(), and nzmath.matrix.MatrixRing._getOne().

◆ _zero

nzmath.intresidue.IntegerResidueClassRing._zero

private

Definition at line 333 of file intresidue.py.

Referenced by nzmath.poly.ring.PolynomialRing._get_zero(), nzmath.poly.ring.RationalFunctionField._get_zero(), nzmath.real.RealField._getZero(), nzmath.intresidue.IntegerResidueClassRing._getZero(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables._getZero(), nzmath.ring.ResidueClassRing._getZero(), nzmath.rational.RationalField._getZero(), nzmath.rational.IntegerRing._getZero(), and nzmath.matrix.MatrixRing._getZero().

◆ isdomain

def nzmath.intresidue.IntegerResidueClassRing.isdomain = isfield

static

Definition at line 296 of file intresidue.py.

◆ iseuclidean

def nzmath.intresidue.IntegerResidueClassRing.iseuclidean = isfield

static

Definition at line 300 of file intresidue.py.

◆ isnoetherian

def nzmath.intresidue.IntegerResidueClassRing.isnoetherian = isfield

static

Definition at line 297 of file intresidue.py.

◆ ispid

def nzmath.intresidue.IntegerResidueClassRing.ispid = isfield

static

Definition at line 299 of file intresidue.py.

◆ isufd

def nzmath.intresidue.IntegerResidueClassRing.isufd = isfield

static

Definition at line 298 of file intresidue.py.

◆ m

nzmath.intresidue.IntegerResidueClassRing.m

Definition at line 230 of file intresidue.py.

Property Documentation

◆ one

nzmath.intresidue.IntegerResidueClassRing.one = property(_getOne, None, None, "multiplicative unit.")

static

Definition at line 328 of file intresidue.py.

Referenced by nzmath.ring.Field.gcd(), nzmath.finitefield.FiniteField.Legendre(), nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FiniteField.sqrt(), nzmath.finitefield.FiniteField.TonelliShanks(), and nzmath.matrix.MatrixRing.unitMatrix().

◆ zero

nzmath.intresidue.IntegerResidueClassRing.zero = property(_getZero, None, None, "additive unit.")

static

Definition at line 336 of file intresidue.py.

Referenced by nzmath.ring.Field.gcd(), and nzmath.matrix.MatrixRing.zeroMatrix().

The documentation for this class was generated from the following file:

nzmath/intresidue.py

Public Member Functions

Public Attributes

Static Public Attributes

Properties

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ __init__()

Member Function Documentation

◆ __contains__()

◆ __eq__()

◆ __hash__()

◆ __ne__()

◆ __repr__()

◆ __str__()

◆ _getOne()

◆ _getZero()

◆ card()

◆ createElement()

◆ getCharacteristic()

◆ getInstance()

◆ isfield()

◆ issubring()

◆ issuperring()

Member Data Documentation

◆ _instances

◆ _one

◆ _zero

◆ isdomain

◆ iseuclidean

◆ isnoetherian

◆ ispid

◆ isufd

◆ m

Property Documentation

◆ one

◆ zero

◆ init()

◆ contains()

◆ eq()

◆ hash()

◆ ne()

◆ repr()

◆ str()